A curve which has the shape of a petalled flower. This curve was named Rhodonea by the Italian mathematician Guido
Grandi between 1723 and 1728 because it resembles a rose (MacTutor Archive). The polar equation of the rose is

or

If is Odd, the rose is -petalled. If is Even, the rose is -petalled. If is Irrational, then there are an infinite number of petals.

The Quadrifolium is the rose with . The rose is the Radial Curve of the Epicycloid.

**References**

Lawrence, J. D. *A Catalog of Special Plane Curves.* New York: Dover, pp. 175-177, 1972.

Lee, X. ``Rose.'' http://www.best.com/~xah/SpecialPlaneCurves_dir/Rose_dir/rose.html.

MacTutor History of Mathematics Archive. ``Rhodonea Curves.'' http://www-groups.dcs.st-and.ac.uk/~history/Curves/Rhodonea.html.

Wagon, S. ``Roses.'' §4.1 in *Mathematica in Action.* New York: W. H. Freeman, pp. 96-102, 1991.

© 1996-9

1999-05-25